Pavel Pogrebnyak and Kaspars Gorkss had the Royals 2-0 to the good inside the opening 12 minutes of the Sky Bet Championship clash, but Simon Cox and sub Darius Henderson clawed Forest level, before Obita's crucial late strike.
Reading ended the game with 10 men as former Red Chris Gunter was sent off, but Nigel Adkins' side held on for a precious win.
Ex-Forest midfielder Garath McCleary set up the Reading opener after just nine minutes as he skipped past the challenge of Dan Harding, before whipping a low centre across the area where Pogrebnyak bundled the ball home at the far post.
Obita then tricked his way into the home box, before crashing a shot into the side netting, with the aid of a deflection.
From the resulting 12th-minute corner, the Royals increased their lead as centre-back Gorkss met Danny Guthrie's kick with a powerful header to stun the home crowd into silence.
It had been a dreadful opening period for Forest, but they finally settled into a rhythm without ever really looking threatening as Reading kept them at arm's reach.
Cox should have reduced the deficit after half an hour, with Forest's first real shot on goal, but his effort from six yards was brilliantly saved by goalkeeper Alex McCarthy. The rebound fell to Henri Lansbury, who curled a shot narrowly wide.
Five minutes before the interval, Forest reduced the arrears as Lansbury's delightful ball sent Jamie Mackie tearing down the right wing and with Cox steaming into the box, Mackie delivered pin-point for his strike partner to crash home unmarked at the back post against his old club.
Reds boss Billy Davies made two changes at half-time, bringing on Andy Reid and Henderson in place of Jamie Paterson and Raddy Majewski, and Henderson almost made an immediate impact by clipping the bar with a thunderous effort.
Reading were starting to wobble as Forest upped the tempo and Mackie brought another save out of McCarthy, with the Royals stopper tipping his header over.
And the pressure told as Henderson danced his way into the area and fired home a low shot to make it all square on the hour mark.
Another Forest break saw Cox play in Mackie, whose rasping drive came back off the bar and bounce the wrong side of the line as the visitors cleared the danger.
After being outplayed for much of the half, Reading silenced the Forest fans again by reclaiming the lead in the 74th minute as they finally mustered a meaningful attack, with Obita crashing home a shot from 12 yards following another McCleary assist.
Reading then handed Forest a lifeline with 10 minutes left as Gunter was shown a second yellow card after tripping Mackie on the edge of the box.
Lansbury had a late effort deflect just wide at the death, but they failed to find the equaliser their efforts deserved.